There is known, for the purpose of stressing workpieces which are to be machined, to use hydraulically operated stretching mechanisms, in which a portion of the thin-walled inner bore is loaded with a stressing pressure by means of a hydraulic medium and the workpiece is thus tightly stressed. This known stretch-stresser, which only permits a slight deviation of the nominal diameter of the workpiece, operates only satisfactorily when a constant ambient state prevails, which under normal working conditions cannot always be guaranteed. For example, with minor leaking losses of the hydraulic medium or when an upper or lower temperture limit is exceeded, the stress safety can longer be maintained. When the plant operation is down such stretch-stressing machines must be kept in chambers with predetermined constant temperature in order to permit the start-up of the machine when restarting the plant. The slightest leak, which has been described hereinabove, inhibits the stress safety, and requires, furthermore, costly and time-consuming repairs.